Perform the following calculation and express the answer to the proper number of significant figures. 100.2 – 0.07 - 76.00 Report your answer in scientific notation using the following form: 1.23 x 104 would be reported as 1.23x10^4 (no spaces).
Perform the following calculation and express the answer to the proper number of significant figures. 100.2 – 0.07 - 76.00 Report your answer in scientific notation using the following form: 1.23 x 104 would be reported as 1.23x10^4 (no spaces).
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Scientific Notation and Significant Figures Calculation**
Perform the following calculation and express the answer to the proper number of significant figures.
\[ \frac{100.2 - 0.07}{76.00} \]
=
Report your answer in scientific notation using the following form:
\[ 1.23 \times 10^4 \]
would be reported as 1.23x10^4 (no spaces).
\[ \_\_\_\_\_\_\_\_\_ \] (Answer box to input the result)
---
### Explanation of the Calculation:
1. **Subtraction in the Numerator:**
- First, perform the subtraction in the numerator: \( 100.2 - 0.07 \).
- \( 100.2 - 0.07 = 100.13 \).
2. **Division by the Denominator:**
- Next, divide the result by the denominator: \( 100.13 / 76.00 \).
- \( 100.13 / 76.00 \approx 1.317763158 \).
3. **Significant Figures:**
- The values used in the calculation have the following significant figures:
- \( 100.2 \) has 4 significant figures.
- \( 0.07 \) has 2 significant figures.
- \( 76.00 \) has 4 significant figures.
- The result of the subtraction \( 100.13 \) should have 4 significant figures.
- In division, the final answer should have the same number of significant figures as the value with the least number of significant figures used in the calculation. Here, the limiting factor is \( 0.07 \) with 2 significant figures.
- Therefore, the final result should be rounded to 2 significant figures.
4. **Scientific Notation:**
- Convert the rounded answer to scientific notation.
- \( 1.32 \) (rounded to 2 significant figures) as the result.
5. **Final Answer:**
- \( 1.32 \) is already in the proper form, and \( 10^0 \) since it's close to 1.
- Thus, the final answer in the required scientific notation is \( 1.3 \times 10^0 \).
**Input Example:**
- The answer should be written in the form `1.3x10^](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3639a026-4183-4e86-95e9-5c63b6a0510f%2F8772df51-c478-4755-88b5-5f706f6bdac1%2Fqp5lgrs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Scientific Notation and Significant Figures Calculation**
Perform the following calculation and express the answer to the proper number of significant figures.
\[ \frac{100.2 - 0.07}{76.00} \]
=
Report your answer in scientific notation using the following form:
\[ 1.23 \times 10^4 \]
would be reported as 1.23x10^4 (no spaces).
\[ \_\_\_\_\_\_\_\_\_ \] (Answer box to input the result)
---
### Explanation of the Calculation:
1. **Subtraction in the Numerator:**
- First, perform the subtraction in the numerator: \( 100.2 - 0.07 \).
- \( 100.2 - 0.07 = 100.13 \).
2. **Division by the Denominator:**
- Next, divide the result by the denominator: \( 100.13 / 76.00 \).
- \( 100.13 / 76.00 \approx 1.317763158 \).
3. **Significant Figures:**
- The values used in the calculation have the following significant figures:
- \( 100.2 \) has 4 significant figures.
- \( 0.07 \) has 2 significant figures.
- \( 76.00 \) has 4 significant figures.
- The result of the subtraction \( 100.13 \) should have 4 significant figures.
- In division, the final answer should have the same number of significant figures as the value with the least number of significant figures used in the calculation. Here, the limiting factor is \( 0.07 \) with 2 significant figures.
- Therefore, the final result should be rounded to 2 significant figures.
4. **Scientific Notation:**
- Convert the rounded answer to scientific notation.
- \( 1.32 \) (rounded to 2 significant figures) as the result.
5. **Final Answer:**
- \( 1.32 \) is already in the proper form, and \( 10^0 \) since it's close to 1.
- Thus, the final answer in the required scientific notation is \( 1.3 \times 10^0 \).
**Input Example:**
- The answer should be written in the form `1.3x10^
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